Quality Control charts range

Figure 1 taken from the petroleum industry shows a quality control chart where the data in the frequency histogram is normally distributed. In this particular control chart, the grand average is 7.08 and is surrounded by + 1, 2, 3 standard deviations rather than range values. 

Of these three measures of variability, the range is much used for small samples (n not greater than 10) in process control work (the quality control chart, discussed in Chapter VIII) on account of its arithmetical simplicity. It is clear that it does not utilise the whole of the information from the data, for the detail of the intermediate results does not enter into the determination. 

The usage of quality control charts in the field of quality assurance is based on the assumption that the determined results are distributed normally. Typical control charts used in a LIMS for routine analysis are, for example, the Shewhart charts for mean and blank value control, the retrieval frequency control chart, and the range and single-value control chart [19]. Quality regulation charts can be displayed graphically in the system or exported to spreadsheet programs. 

Fig. 9. Quality control chart for range (H2). (Courtesy Elsevier Publishing Co., Amsterdam.)...

Figure 9 illustrates the use of the quality control chart for the range in connection with the previously mentioned problem on the incorporation of Amatol. The Hooo and control limits are shown, and ranges outside of these limits would occur by chance one time in a thousand and one time in 40, respectively. 

Methods for using quality control charts, for both standard deviation and range, are discussed and illustrated with reworked data from Lowry s report (L4). This is discussed in Section III, C, 6. Numbers 13 and 14 are also mentioned in Herdan (H2) but no reference is given. 

A quality control chart is a time plot of a measured quantity that is assumed to be constant (with a Gaussian distribution) for the purpose of ascertaining that the measurement remains within a statistically acceptable range. It may be a day-to-day plot of the measured value of a standard that is run intermittently with samples. The control chart consists of a central line representing the known or assumed value of the control and either one or two pairs of limit lines, the inner and outer control limits. Usually the standard deviation of the procedure is known (a good estimate of cr), and this is used to establish the control limits. 

Control charts were originally developed in the 1920s as a quality assurance tool for the control of manufactured products.Two types of control charts are commonly used in quality assurance a property control chart in which results for single measurements, or the means for several replicate measurements, are plotted sequentially and a precision control chart in which ranges or standard deviations are plotted sequentially. In either case, the control chart consists of a line representing the mean value for the measured property or the precision, and two or more boundary lines whose positions are determined by the precision of the measurement process. The position of the data points about the boundary lines determines whether the system is in statistical control. 

Control charts based on variable sample data include the x chart and the. v chart. When dealing with a numerically measurable quality characteristic, the x chart is usually employed to monitor the process average and the s chart is used to monitor the process variability. When there is only one observation in each sample, the individual measurement chart (I chart) and moving range chart (MR chart) are used to monitor the process average and variability. It should be noted that due to the poor... 

All uncertainty estimates start with that associated with the repeatability of a measured value obtained on the unknown. It is neither required for the sake of quality control, nor could it always be economically justified, to make redundant determinations of each measured value, such as would be needed for complete statistical control. Repeat measurements of a similar kind under the laboratory s typical working conditions may have given satisfactory experience regarding the range of values obtained under normal operational variations of measurement conditions such as time intervals, stability of measurement equipment, laboratory temperature and humidity, small disparities associated with different operators, etc. Repeatability of routine measurements of the same or similar types is established by the use of RMs on which repeat measurements are made periodically and monitored by use of control charts, in order to establish the laboratory s ability to repeat measurements (see sect, entitled The responsible laboratory above). For this purpose, it is particularly important not to reject any outlier, unless cause for its deviation has been unequivocally established as an abnormal blunder. Rejection of other outliers leads a laboratory to assess its capabilities too optimistically. The repeatability in the field of a certified RM value represents the low limit of uncertainty for any similar value measured there. 

Fig. 2. Shewhart mean and range charts for valproic acid using the data shown in Fig. 1 and similar data from high, mid, and low pools of quality control serum, against occasion of analysis. -----------------=95% limits ---------------=99% limits...

Samples can be divided into two aliquots and analyzed, and the duplicates used for control purposes. This is a simple quality control procedure that does not require stable control materials and therefore can be used when stable materials are not available or as a supplemental procedure when stable control materials are available. The differences between duplicates are plotted on a range type of control chart that has limits calculated from the standard deviation of the differences. When the duplicates are obtained from the same method, this range chart monitors only random error and thus is not adequate for ensuring the accuracy of the analytical method. When the duplicates are obtained from two different laboratory methods, then the range chart actually monitors both random and systematic errors but cannot separate the two types of errors. The interpretation becomes more difficult, particularly when there are stable systematic differences or biases between the two analytical methods. Multiplicative factors may be necessary to deal with proportional differences, and additive factors may be necessary to allow for constant differences. Interpretation of observed differences becomes more qualitative nevertheless, this procedure still provides a useful way of monitoring the consistency of the data being generated by the laboratory. 

A conventional response to issues of variability in bioassays is to construct Shewhart Control Charts based on the results achieved in repeat tests within a laboratory using a reference toxicant. This effectively describes the range of results typically found within the laboratory and hence can be used to define limits within which the laboratory normally expects to operate. However, there is a flaw in such internal quality control because the more variable a laboratory s reference toxicant test results are, the wider the limits of acceptability will be. Indeed, it can serve merely to reinforce high variability or bias. 

Good laboratory—what it is, how to apply it, p. 125 e How to vahdate a method selectivity, hnearity, accuracy, precision, sensitivity, range, LOD, LOQ, ruggedness, p. 126 Quality assurance control charts, documenting, proficiency testing, p. 133 Electronic records, p. 135... 

Standard quality control manuals provide detailed information on setting up and evaluating control charts. Generally, three situations can be detected and corrected using the mean and range charts in tandem ... 

Statistical control applies to all parts of the analytical system - sampling process, the calibration, the blank, and the measurement. Statistical control is attained by the quality control of the entire system and Involves maintenance of realistic tolerances for all critical operations. A system of control charts is the best way to demonstrate attainment of statistical control and to evaluate the appropriate standard deviations. In the simplest form, the results of measurement of a stable check sample, obtained over a period of time, are plotted. Statistical control is demonstrated when the values are randomly distributed around their average value." Control limits are often taken as 2 or 3 standard deviation units of these replicates. Dr. Taylor also adds, "Even the ranges of duplicate measurements of the actual samples tested can be plotted in a similar manner to demonstrate a stable standard deviation. In either case, the statistics of the control charts are the best descriptors of the variability of the measurement process."... 

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